Quantum theory-based continuous precision nmr/mri: method and apparatus

ABSTRACT

A method for spin magnetic resonance applications in general, and for performing NMR (nuclear magnetic resonance spectroscopy) and MRI (nuclear magnetic resonance imaging) in particular is disclosed. It is a quantum theory—based continuous precision method. This method directly makes use of spin magnetic resonance random emissions to generate its auto-correlation function and power spectrum, from which are derived the relaxation times and spin number density. The method substantially reduces the NMR/MRI machine and data processing complexity, thereby making NMR/MRI machines much less-costly, much less-bulky, more accurate, and easier to operate than the current pulsed NMR/MRI. By employing extremely low transverse RF magnetic B 1  field (around or less 0.01 Gauss), MRI with this method is much safer for patients. And, by employing continuous spin magnetic resonance emissions, NMR with this method is of virtually unlimited spectral resolution to satisfy any science and engineering requirements.

CROSS REFERENCE TO RELATED APPLICATIONS

This application claims priority from U.S. Provisional Application Ser. No. 60/915,661, filed May 2, 2007 and from U.S. Provisional Application Ser. No. 60/943,802, filed Jun. 13, 2007, the contents of which are incorporated herein in their entireties.

FIELD OF THE INVENTION

This invention relates to spin magnetic resonance in general, and nuclear spin magnetic resonance spectroscopy (NMR)/nuclear spin magnetic resonance imaging (MRI) in particular. It describes a method and apparatus for spin magnetic resonance data generation, data acquisition, and data reduction.

BACKGROUND OF THE INVENTION

Since the discovery of nuclear spin magnetic resonance in condensed matter independently by Bloch [1] and Purcell [2] some 60 years ago, it has been rapidly evolved into a primary research and engineering technique and instrumentation in physics, chemistry, biology, pharmaceutics, etc. Particularly after pioneering work by Damadian [3] and Lauterbur [4] in the early 1970s, its developments in medicine have revolutionized diagnostic imaging technology in medical and health sciences.

Basically there are two broad categories in nuclear magnetic resonance applications. One is nuclear magnetic resonance spectroscopy (spectrometer); the other is nuclear magnetic resonance imaging (scanner). Both of them need a strong static magnetic field B_(o). They share the same physical principles, mathematical equations, and much of data acquisition and processing techniques, but their focuses and final outcomes are different. To avoid confusion, following conventions adopted in academia and industries, in this application the acronym “NMR” will be used for nuclear magnetic resonance spectroscopy (spectrometer); and the acronym “MRI” will be used for nuclear magnetic resonance imaging (scanner). NMRs are often used in chemical, physical and pharmaceutical laboratories to obtain the spin magnetic resonant frequencies, chemical shifts, and detailed spectra of samples; while MRIs are often used in medical facilities and biological laboratories to produce 1-D (one dimensional), 2-D (two dimensional), or 3-D (three dimensional) imagines of nuclear spin number density ρ, spin-lattice relaxation time T₁, and spin-spin relaxation time T₂ of human bodies or other in vivo samples. There have been two parallel theoretical treatments of nuclear spin magnetic resonance [5]. One, based upon quantum mechanics [5, 6], is thorough and exhaustive; the other, based on semi-classical electromagnetism [5, 7], is phenomenological. These two descriptions are complementary. The quantum mechanics descriptions can be quantitatively applied to all known phenomena in nuclear magnetic resonance; the classical theories are useful to explain most experiments in nuclear magnetic resonance except some subtle ones. Nevertheless, when it comes to practical applications, the classical theories dominate. The classical Bloch equations combined with radio frequency (RF) B₁ field pulses, spin and gradient echoes, spatial encoding, and free induction decay (FID) constitute much of the so-called pulsed nuclear magnetic resonance today. Modern nuclear spin magnetic resonance applications are virtually entirely theorized and formulated on classical electromagnetics [8].

SUMMARY OF THE INVENTION

This invention provides a novel system, i.e., method and apparatus for conducting NMR and MRI investigations. The basic individual equipment and hardware required by this method are much the same as those used in a conventional pulsed NMR/MRI. However, unlike conventional methods, the present invention is a continuous precision method, for conducting NMR and MRI applications. The invention is based on quantum theories of radiation, its physics and mathematics are accurate and rigorous; and it works in a continuous mode, and as such distinguishes itself over conventional pulsed NMR and MRI in almost all aspects from principles and equations to data generation, acquisition and reduction. In the practice of the present invention magnetization M of the sample under study plays no roles at all, and the uses of pulses, phases, echoes, and FID are avoided. Thus, the intimate relationships between signal strength/SNR (signal-to-noise ratio) and the static field B_(o) essentially have been eliminated. Instead what matters in this continuous method is the quantum transition probability P between two spin Zeeman energy levels in the static magnetic field B₀. The system sensitivity and SNR is greatly enhanced through auto/cross-correlation. Consequently, this continuous precision method is capable to be applied to both high- and low-magnetic field NMR/MRI.

BRIEF DESCRIPTION OF THE DRAWINGS

Further features and advantages of the present invention will be seen from the following detailed description, taken in conjunction with the accompanying drawings wherein like numerals depict like parts, and wherein

FIG. 1 a is a plot of spin energy in a magnetic field;

FIG. 1 b shows magnetic field orientation;

FIG. 2 is a plot showing relationship between relaxation times, emission probabilities and signals;

FIG. 3 a and FIG. 3 b schematically illustrate receiver coil sets in accordance with the present invention;

FIG. 4 schematically illustrates data acquisition and data reduction in accordance with the present invention;

FIG. 5 a and FIG. 5 b illustrate frequency-encoding magnetic field for spin spatial localization in accordance with the present invention;

FIG. 6 schematically illustrates data acquisition and data reduction in accordance with the present invention;

FIG. 7 a, FIG. 7 b and FIG. 7 c schematically illustrate single receiver coil embodiments and correction boxes in accordance with the present invention; and

FIGS. 8 a, 8 b and 8 c graphically illustrate correction of correlation function in accordance with the present invention.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

This disclosure concerns spin magnetic resonance in general, and nuclear spin magnetic resonance spectroscopy (NMR) and nuclear spin magnetic resonance imaging (MRI) in particular, and describes and provides a system, i.e., method and apparatus for performing nuclear spin magnetic resonance applications.

By nature, spin magnetic resonance is a quantum phenomenon. From this perspective, a novel method and technology for NMR and MRI has been developed. Its theoretical basis is the quantum theories of radiation; its physics and mathematics are accurate and rigorous; and it works in continuous mode. Consequently, this method distinguishes itself over the conventional pulsed NMR/MRI in almost all aspects from principles and equations to data generation, acquisition, and reduction.

As contrasted with conventional pulsed NMR and MRI, this method of invention utilizes, in a direct and natural manner, continuous stationary random noise as signals from the spin magnetic resonance transition emissions. Those, such as magnetization M, pulses, phases, echoes, free induction decay (FID), that play important roles in pulsed NMR and MRI play no roles and actually are all discarded in this continuous precision NMR and MRI. Instead, what matters in this invention is the spin magnetic resonance emission signal V_(SR)(t) itself, which is continuous, stationary (ergodic), and random. According to the present invention, this random signal V_(SR)(t), in its original appearance and without any manipulations, can be explored to reveal rich information on spin resonance spectrum S(ν), spin number density ρ, and relaxation times T₁ and T₂.

Two key functions in this invention are the auto-correlation function R(t) and the power spectrum S(ν) of the spin magnetic resonance random emissions. From R(t) and S(ν) other NMR or MRI parameters can be derived using Eqs. (3, 6, 7 and 8) as will be discussed below. The Wiener-Khinchin theorem, Eq. (5), relates R(t) to S(ν). From R(t) to S(ν) is a forward Fourier transform; while from S(ν) to R(t) is an inverse Fourier transform. Therefore, either R(t) or S(ν) can be firstly obtained from the spin emission random signal V(t). There are various ways and commercially available computer software to calculate R(t) and S(ν) [12]. In this invention disclosure, the correlation function R(t) is first obtained from spin resonance noise signal V(t), then Eq. (5) yields S(ν). In this sequence, the non-signal random noises in V(t) can be eliminated in the auto/cross-correlation operation. If first obtaining S(ν) from V(t) and secondly obtaining R(t) from S(ν) with an inverse Fourier transform, this S(ν) is contaminated by all non-signal noises and other unwanted signals.

Auto/cross-correlation needs two signals as its inputs, and outputs their auto/cross correlation function. For this purpose, a unique, two identical sets of receiver coils may be employed in this invention. FIGS. 3 a and 3 b as will be described below in greater detail conceptually depict these twin sets of coils, showing two possible configurations. These two sets of receiver coils are placed together surrounding the NMR/MRI sample, generating two voltages V_(a)(t) and V_(b)(t) at the two sets of coil terminals. V_(a)(t) and V_(b)(t) in fact contains the spin resonance emission signal noise V_(SRa)(t) and V_(SRb)(t), other electronic random noises V_(Na)(t) and V_(Nb)(t), and the RF B₁ field-related voltage V_(B1a)(t) and V_(B1b)(t). V_(Na)(t) and V_(Nb)(t) are going to be cancelled out in cross-correlation operation, because of their statistically independency. V_(SRa)(t)=V_(SRb)(t); V_(B1a)(t)=V_(B1b)(t), but V_(B1a)(t) and V_(B1b)(t) are not random. They cannot be eliminated in the correlation operation, but their contributions to the contaminated auto-correlation function R′(t) can be removed in the “correction R′(t) for R(t)” shown in FIGS. 4, 6, and 7 a-7 c as will be discussed below in greater detail.

There are two possible embodiments of this method of invention as sketched out in FIGS. 4 and 6 for double sets of receiver coils and in FIGS. 7 a-7 c for a single set of receiver coils. The single set of receiver coils in this disclosure is the same as that used in the conventional pulsed NMR/MRI. The embodiments with a single set of coils of FIGS. 7 a-7 c take less hardware, but elimination of non-signal noises with correlation is not possible (FIG. 7 a) or only partially (FIGS. 7 b and 7 c). The clearing away of these non-signal noises takes place in the “Correction R′(t) for R(t)” function block (FIGS. 7 a-7 c).

The transverse RF magnetic field B₁ in this invention is necessary for measurements of the relaxation time T₂; but if only the relaxation time T₁ is required, measurements can be also carried out without the B₁ field. In either case, this RF field B₁ has to be continuous and steady. Applying this field B₁ alters the spin ensemble to another dynamic equilibrium state through stimulating extra resonance transition probability P_(B1). This is an effective way to enhance spin signal strength. In any situations, however, a very weak B₁ field, on the order of 0.01 Gauss or less, is desired.

The primary outcomes of this NMR/MRI operating method are the spin magnetic resonance emission power spectrum S(u), spin number density ρ, relaxation times T₁ and T₂, and their images. All these parameters are of their true values, not the so-called “weighted” p, “weighted” T₁, and “weighted” T₂.

Through using a weak RF field B₁ to augment the strength of the spin emission signals and using auto/cross-correlation to diminish the non-signal noises, this invention not only makes high static magnetic field B_(o) unnecessary, but also use fewer hardware and software. Consequently, NMR/MRI machines with this method are much less-costly, much less-complex, much less-bulky, and safer, more accurate, higher spectral resolution, easier to operate than the current pulsed NMR/MRI, thus bringing about broad applications to science, including medical science, and engineering.

The description of a pulsed NMR or MRI is in terms of the magnetization vector M of material under study in a static magnetic field B_(o), its precession around the field B_(o), and the free induction decay (FID) signals. The description of quantum theory-based continuous NMR and MRI of this invention is in terms of spin population distributions, Zeeman splitting of spin energy in the magnetic field B₀, transition probabilities between the Zeeman energy levels, and the spin magnetic resonance random emission noise. Every atom possesses a nucleus. Each nucleus is composed of proton(s) and neutron(s), except ordinary hydrogen nucleus ¹H that holds only one proton and no neutron. If a nucleus has at least one unpaired proton or neutron, its mechanical spin about an axis gives rise to a spin magnetic moment μ=γh√{square root over (I(I+1))}, where γ and h are known as the spin gyro-magnetic ratio and Planck's constant, respectively. Letter I denotes the spin quantum number. The most frequently used nucleus in MRI seems to be proton ¹H; the most frequently used nuclei in NMR seem to be proton ¹H and carbon-13 ¹³C. Spin quantum number I of ¹H and ¹³C is both equal to ½. The gyro-magnetic ratio γ of ¹H and ¹³C equals 2.675×10⁸ rad sec⁻¹ Tesla⁻¹ and 6.729×10⁷ rad sec⁻¹ Tesla⁻¹, respectively. Magnetic spins do not have any preferred spatial orientation in a zero-magnetic field environment. When an ensemble of nuclear magnetic spins is placed in the static magnetic field B_(o) whose direction is designated as the z-axis of a Cartesian coordinate system, the originally-degenerate spin magnetic energy levels split into (2I+1) equally separated Zeeman energy levels. For ¹H or ¹³C case I=½, there are only (2I+1)=2 Zeeman levels. The high energy (upper) level is E_(h) and the low energy (lower) level is E_(l), as shown in FIG. 1 a. Accompanying the energy splitting, spatial quantization of the spins takes place. Those spins of energy E₁ align themselves towards the positive B_(o) direction; while those spins of energy E_(h) align themselves towards the negative B_(o) direction (FIG. 1 b). When thermal equilibrium establishes, spin number density n_(h) at the upper level and spin number density n_(l) at the lower level satisfy the Boltzmann distribution: n_(h)/n_(i)=exp(−γh₀/2πk_(B)T), where h is Planck's constant; and k_(B) and T denote Boltzmann's constant and spin temperature, respectively. Although always n_(l)>n_(h), n, is almost equal to n_(h), meaning (n_(l)−n_(h))(n_(h)+n_(l)) is a very small number no matter how strong the B_(o) field would be in a typical laboratory environment. The difference (n_(l)−n_(h)) depends upon the strength of B_(o). Larger B_(o) results in larger (n_(l)−n_(h)), and larger (n_(l)−n_(h)) in turn results in a larger magnetization M of the sample and a higher Larmor frequency. This is one of the main reasons that the pulsed NMR/MRI tends to utilize a higher B_(o). The present invention does not use the magnetization M and the difference (n_(l)−n_(h)), so a high B_(o) field does not necessarily mean better NMR/MRI performance.

Although in thermal equilibrium, the higher- and lower-level spin number densities n_(h) and n_(l) remain in steady state as long as field B_(o) and temperature T remain unchanged, the spins at the upper energy level continuously, due to the spin-lattice interactions, transit to the lower energy level with a transition probability P_(Bo) and vice versa, so that statistically dn_(h)/dt=dn_(l)/dt=0. This is referred to as a “dynamic equilibrium”. Each spin higher-to-lower level transition accompanies an emission of a photon of angular frequency—the Larmor frequency—ω_(o)=γB_(o) (the linear frequency ν=ω/2π in Hertz.) Each such emission of a photon induces a microscopic voltage at the terminals of nearby detection devices (receiver coils) that surround the sample in study. Adding up all these emissions, macroscopic spin magnetic resonance emission signals are established. This process is a random process. The established signals appear in the form of stationary (ergodic) random noise. These noises are intrinsically weak, yet measurable with modern electronics. The time sequence of this noise constitutes the continuous stationary (ergodic) random noise signal V_(Bo)(t) of nuclear spin magnetic resonance emissions at receiver coil's output terminals.

The above spin resonance random emissions in the magnetic field B_(o) occur in a natural and continuous manner, no matter whether the transverse RF magnetic field B₁ presents or not. From quantum mechanics view, the role of the transverse RF field B₁ at the Larmor frequency is to stimulate extra random emissions with transition probability P_(B1) between the same two spin Zeeman energy levels, resulting in an extra spin resonance emission noise signal V_(B1)(t). Because of the statistical independency between the emissions due to B_(o) and due to B₁, provided that B_(o) and B₁ both are present, the total spin resonance transition probability P_(SR)=P_(Bo)+P_(B1), and the combined spin magnetic resonance emission noise signal V_(SR)(t)=V_(Bo)(t)+V_(B1)(t) (FIG. 2). If being analyzed properly, this time sequence of the spin resonance emission random noise signal of V_(SR)(t) would reveal rich and detailed information on the spin transition probabilities, relaxation times, resonance spectra, etc.

The transition probability P governs its transition rate between two energy levels (FIG. 2). The dimension of P is 1/second, its reciprocal is the relaxation time T (sec), i.e., T=1/P. The reciprocal of P_(Bo) is the spin-lattice relaxation time T₁, the reciprocal of P_(B1) is relaxation time T_(B1) (T_(B1) is not the spin-spin relaxation time T₂), and the reciprocal of P_(SR) is relaxation time T_(SR). Since P_(SR)=P_(Bo)+P_(B1), so 1/T_(SR)=1/T₁+1/T_(B1) (FIG. 2).

If the spin number density at the upper energy level is n_(h) and its corresponding transition probability is P, the number of transitions from the upper level to the lower level per second equals n_(h)×P. Then the resonance emission power W(t) may be expressed as W(t)=hν_(o)n_(h)P, here h and ν_(o) represent Planck's constant and the Larmor frequency. W(t) is proportional to the squared noise voltage V(t). Thus increasing P leads to a greater resonance noise signal V(t).

As long as field B_(o) and temperature T remain unchanged, the probability P_(Bo) and the spin-lattice relaxation time T₁ are main constant. When the field B₁ is applied, as described below, the probability P_(B1) varies with B₁ squared. Comparing with the RF field B₁, the static magnetic field B_(o) takes very mildly roles in increasing or decreasing its spin transition probability P_(Bo).

The Larmor frequency B₁-stimulated Zeeman transition probability is denoted by P_(B1). Provided that the field B₁ is much weaker than the field B_(o) (this is always the case in NMR and MRI), its effect on the energy Hamiltonian of the spin ensemble can be considered as a perturbation. Then the standard quantum mechanics perturbation theory applies, resulting in an expression relating the spin-spin relaxation time T₂ and field B₁ to the B₁-stimulated transition probability P_(B1)[9,10]:

$\begin{matrix} {{P_{B\; 1} = {\frac{1}{2}\gamma^{2}{B_{1}^{2}\left( {I + m} \right)}\left( {I - m + 1} \right)T_{2}}},} & (1) \end{matrix}$

where again γ and I are the gyro-magnetic ratio and the spin quantum number, respectively. Symbol m is the spin magnetic quantum numbers. For all I=½ (then m=½) nuclei, such as proton (¹H), carbon-13 (¹³C), or phosphorus-31 (³¹P), the above equation reduces to [9],

$\begin{matrix} {{P_{B\; 1} = {\frac{1}{2}\gamma^{2}B_{1}^{2}T_{2}}},} & (2) \end{matrix}$

When both the static field B₀ and the transverse RF field B₁ at the Larmor frequency applied, because of statistical independency, the composite spin resonance transition probability P_(SR)=P_(Bo)+P_(B1). Therefore, in terms of relaxation times,

$\begin{matrix} {{\frac{1}{T_{SR}} = {{\frac{1}{T_{Bo}} + \frac{1}{T_{B\; 1}}} = {\frac{1}{T_{1}} + {\frac{1}{2}\gamma^{2}B_{1}^{2}T_{2}}}}},} & (3) \end{matrix}$

where T₁ and T₂ are spin-lattice and spin-spin relaxation times, respectively.

Eq. (3) is a key equation in this invention that establishes the relationship among a priori known field B₁, quantity T_(SR), and the relaxation time T₁ and T₂. When both B₀ and B₁ presented, the composite spin magnetic resonance signal V_(SR)(t)=V_(Bo)(t)+V_(B1)(t). The noise signal V_(Bo)(t) contains information on the relaxation time T₁; the noise signal V_(B1)(t) contains information on the relaxation time T₂. The combined continuous stationary random noise signal V_(SR)(t), whose relaxation time is T_(SR), contains information on both T₁ and T₂.

Assume a stationary random time signal V(t), which may represent V_(Bo)(t) or V_(B1)(t) or V_(SR)(t)=V_(Bo)(t)+V_(B1)(t); its auto-correlation function R(t) is defined as:

$\begin{matrix} {{R(t)} = {\lim\limits_{T->\infty}{\frac{1}{T}{\int_{0}^{T}{{V(\tau)}{V\left( {t + \tau} \right)}{\tau}}}}}} & (4) \end{matrix}$

R(t) is a real-valued even function, R(t)=R(−t). After this auto-correlation function, the power spectrum S(ν) and relaxation time T of the signal V(t) can be strictly derived with two mathematical theorems:

The Wiener-Khinchin theorem, which states that the power spectrum S(ν) of a time function V(t) is the Fourier transform of its auto-correlation function R(t) [11,12].

$\begin{matrix} {{{S(v)} = {\int_{- \infty}^{+ \infty}{{R(t)}{\exp \left( {{- j}\; 2\pi \; t\; v} \right)}{\tau}}}},} & (5) \end{matrix}$

where j=(−1)^(1/2), ν is frequency. Once having the power spectrum S(ν), spin resonance frequency ν_(o) can be found as [13]

$\begin{matrix} {v_{o} = {\frac{\int_{0}^{\infty}{{S^{2}(v)}{v}}}{\int_{0}^{\infty}{{S^{2}(v)}{v}}}.}} & (6) \end{matrix}$

The Born-Wolf theorem, which states that the squared relaxation time T of a time function V(t) is the normalized second moment of its squared auto-correlation function R(t), [13,14]

$\begin{matrix} {T = \left\lbrack \frac{\int_{0}^{\infty}{t^{2}{R^{2}(t)}{t}}}{\int_{0}^{\infty}{{R^{2}(t)}{t}}} \right\rbrack^{\frac{1}{2}}} & (7) \end{matrix}$

This is another key equation in this invention, since it furnishes an exact way to calculate the relaxation time T.

In addition to the spin relaxation times T₁ and T₂, spin number density ρ is also a fundamental parameter in NMR/MRI applications. The spin density ρ can be derived from the spin transition probability P and the spin resonance power spectrum S(ν) at the resonance frequency ν_(o), since S(ν₀)=c×ρ×P, where c is a calibration factor. Usually the relative spin number density ρ is requested, which leads to the following expression:

Relative spin number density

$\begin{matrix} {\rho = {\frac{S\left( v_{0} \right)}{P} = {{S\left( v_{0} \right)} \times {T.}}}} & (8) \end{matrix}$

Here probability P and T may represent either P_(B1) and T₁ when only B₀ exists, or P_(SR) and T_(SR) if B₁ is applied. In cases the absolute spin number density ρ is demanded, the calibration factor c has to be evaluated.

The above six equations (3, 4, 5, 6, 7 and 8) are the basis of data analysis and data reduction in this invention. In short, after acquisition of the spin magnetic resonance noise signal V_(SR)(t), the spin resonance power spectrum S(ν), resonance frequency ν_(o), spin number density ρ, as well as the relaxation times T_(SR) can all accurately be calculated by making use of Eqs. (3, 4, 5, 6, 7 and 8). Without the field B₁(B₁=0), V_(SR)(t)=V_(B1)(t), P_(SR)=P_(Bo), T_(SR)=T_(Bo)=T₁; with the field B₁, V_(SR)(t)=V_(Bo)(t)+V_(B1)(t), then according to Eq. (3) T_(SR) depends upon T₁ and T₂. Two sets of measurements at two different values of B₁ (one B₁ may be equal to 0) yield two T_(SR) and thus two equations (3), they can be solved simultaneously for T₁ and T₂.

The parameters ρ, T₁, and T₂ calculated here from the above equations and procedures are their “true” values. They are different from the so-called “weighted” T₁, T₂, or p in the pulsed NMR/MRI.

Eq. (7) is actually not the only formula for calculating the relaxation time T of signal V(t) from its auto-correlation function R(t). There could have other mathematical forms accomplishing the same task. For instance, Goodman (15) defines the relaxation time T using the following formula:

$\begin{matrix} {T = {\int_{- \infty}^{\infty}{{{R\; (\tau)}}^{2}\ {{\tau}.}}}} & (9) \end{matrix}$

Both Eqs. (7) and Eq. (9) can be used for determining relaxation time T. Eq. (9) is simpler, but Eq. (7) asserts to be of more physical insight. In this disclosure, calculations of relaxation times are based on Eq. (7).

1. The Transverse RF (Radio-Frequency) Magnetic Field B₁

Similar to pulsed NMR/MRI, this invention employs a transverse (in the x-y plane) RF (radio-frequency) magnetic field B₁ generated by a transmitting coil set. But what differs over the RF field B₁ in the pulsed NMR/MRI is that in the present invention there is a continuous (not pulsed) and very weak B₁ field used for stimulating spin magnetic resonance emissions. It is a broadband (much broader relative to the bandwidths of spin resonance emission lines) alternating magnetic field. Because of the continuous working mode, some of the RF magnetic field B₁ would inevitably be intercepted by the receiver coils and induce some extra voltage U_(B1)(t), additively along with the spin resonance emission noise signal V_(SR)(t). Then U_(B1) and V_(SR) together will be fed up to the following electronics indiscriminately by the receiver coils. U_(B1) is unwanted interference to V_(SR). Thus, it should be suppressed to a minimum level possible. Three individual methods may be applied in succession to virtually eliminate this V_(SR) interference: (1) mechanically constructing receiver coil(s) with special design, installation, and alignment. One arrangement is to make the receiver coil set perpendicular (90 degrees) to the transmitter coil set in order to null the cross-coupling or leaking between them. By this orthogonality, the cross-coupling between the transmitter and receiver coils can be limited to no more than 1%; (2) electronically using some special compensation circuits; and (3) numerically applying some correction techniques to finally eliminate this V_(B1) effects. The detailed description of this third one is discussed below.

In addition to the fraction of B₁ field power directly deposited to the receiver coils due to cross-coupling, there is a possible secondary effect due to the RF B₁ field. The B₁ field generated originally by the transmitter coils can cause some electromagnetic disturbances in the sample volume. Parts of these disturbances possibly may feed back to the receiver coils inducing some secondary U_(B1). In the following description, when U_(B1) is referred to, it always means the sum of these U_(B1) from the direct and the secondary effects.

2. The Receiver Coils for Spin Magnetic Resonance Random Emissions

This continuous NMR/MRI method makes use of two kinds of receiver (detection) coils. One is to use two identical pairs of receiver coil sets to generate two identical spin resonance emission noise signals V_(SRa)(t) and V_(SRb)(t). The other one is to use a single receiver coil set, the same as the one in the pulsed NMR/MRI, to generate a single spin resonance emission noise signal V_(SR)(t). FIGS. 3 a and 3 b illustrate these two pairs of receiver coils that are identical and installed closely. They may be placed on both sides surrounding the sample under study (FIG. 3 a), or wound together around the sample under study (FIG. 3 b). The two terminals of the coil 10 or coil pair 10 feed the signal V_(a)(t) to the electronics 14 and 62; the two terminals of the coil 12 or coil pair 12 feed the signal V_(b)(t) to the electronics 16 and 64 (see FIG. 4 and FIG. 6). Voltages V_(a)(t) and V_(b)(t) are the additive sum of the spin resonance emission signal noise V_(SR)(t), U_(B1)(t), and V_(n)(t). V_(n)(t) here represents all kinds of non-signal random noises (such as the thermal Johnson noise, shot noise, etc.) emanated from the coils (and later from the following electronics). V_(a)(t)=V_(SRa)(t)+U_(B1a)(t)+V_(na)(t) and V_(b)(t)=V_(SRb)(t)+U_(Bsb)(t)+V_(nb)(t). V_(SRa)(t)=V_(SRb)(t) and U_(B1a)(t)=U_(B1b)(t), but V_(na)(t)≠V_(nb)(t). However, these three types of signals, V_(SR)(t), U_(B1)(t) and V_(n)(t), are mutual independent statistically. Furthermore, V_(na)(t) is statistically independent with V_(nb)(t).

3. Description of the Continuous Precision NMR and MRI

The fundamental parameters in NMR or MRI applications are spin magnetic resonance line profile (power spectrum) S(ν), spin number density ρ, spin-lattice (longitudinal) relaxation time T₁, and spin-spin (transverse) relaxation time T₂. Other parameters required in some special NMR/MRI may be derived from these measurements. In general, the above parameters are functions of positions x, y, and z in the sample volume, thus requiring 1-D, 2-D or 3-D imaging. The samples in NMR applications usually are homogeneous throughout the sample volume, rendering these parameters free of variations in the volume.

3-1. Nuclear Magnetic Resonance Spectroscopy (NMR)

The tasks for NMR applications are in general to obtain p, T₁, T₂, and the detailed high-resolution spin resonance spectrum for a homogenous sample under investigation. If spatial distributions of these parameters are sought, it becomes the tasks of magnetic resonance imaging (MRI).

FIG. 4 shows the flowchart for the data generation, acquisition, and reduction in NMR applications. Block 20 contains NMR machine equipment, such as the magnet for field B_(o), RF transmitter coil for radiating the transverse (in the x-y plane) field B₁(block 22), and the receiver coil set. The sample under study is placed in the static field B_(o). There is no gradient field there, since no imaging or spin localization is required. In block 20 of FIG. 4, there are two identical pairs of receiver coil sets as described above and illustrated in FIGS. 3 a and 3 b. After placing a sample in the magnetic field B_(o), magnetic resonance emissions of the spins in the sample naturally occur, and thus generate two signals V_(a)(t) and V_(b)(t) at terminals of each of the two pairs of coil sets. For electronics 14, V_(a)=V_(SRa)+V_(na)+U_(B1a); for electronics 16, V_(b)=V_(SRb)+V_(nb)+U_(B1b). After separately passing through electronics 14 and 16 (electronics 14 and 16 are identical), V_(a)(t) and V_(b)(t) meet in a auto/cross-correlator 24 for correlation. Correlator 24 acts as an auto-correlator for V_(SR) and U_(B1), yielding an auto-correlation function R′(t)=R_(SR)(t) of V_(SR)+R_(B1)(t) of U_(B1), since V_(SRa)=V_(SRb) and U_(B1a)=U_(B1b). For statistically independent V_(na)(t) and V_(nb)(t), correlator 24 acts as a cross-correlator, yielding correlation function R_(n)(t)=0. Thus R′(t)=R_(SR)(t)+R_(B1)(t)+R_(n)(t)=R_(SR)(t)+R_(B1)(t). Only R_(SR)(t) is needed for NMR applications. R_(B1)(t) must be removed from R′(t). This is the task of correction block 26 in FIG. 4 (see below). Its input is the contaminated auto-correlation R′(t), after correction its output is R(t)=R_(SR)(t). This is the case when the static field B_(o) and the RF field B₁ both are present. When the RF field B₁ not applied, U_(B1)(t)=0 and no R_(B1)(t), then correction block 26 becomes unnecessary. This invention uses correlation to eliminate non-signal noises V_(n)(t), hence greatly enhances system's SNR. Correlation works ideally for recovering weak signals submerged in strong independent noise.

Once R(t) has been obtained, the Wiener-Khinchin theorem Eq. (5), and Eq. (6) yield the spin resonance spectrum S(ν) and the spin resonance frequency ν_(o). Eq. (7) precisely calculates the relaxation time T from R(t), and Eq. (8) brings forth the spin number density ρ. (Block 28).

If only S(ν), ρ and T₁ are required, the RF field B₁ in the above procedure is not necessary to apply. Without B₁, S(ν), ρ, and T₁ may come from one set of measurements. On the other hand, if relaxation time T₂ is also needed, the above procedure must repeat twice to generate two R(t) at two different B₁ values (one of the two B₁ values may be set to 0). Two R(t) yield two T_(SR) with Eq. (7). Using these two T_(SR), relaxation times T₁, and T₂ can be obtained by solving two Eq. (3) simultaneously, one for the first B₁ and one for the second B₁.

This transverse RF B₁ field established with the transmitter coil must be uniform throughout the entire sample volume. It is a continuous steady-state RF B₁ field, its bandwidth should be much wider, e.g. ˜3 orders of magnitude wider, than the bandwidths of the spin resonance emissions.

In solving Eq. (3) for T₁ and T₂, the strength of B₁ could affect solution accuracies. According to numerical analysis, the term 1/T₁ should not be too much different from ½ (γB₁)²T₂ in order to keep solutions adequately accurate. Under this consideration, for relaxation times T₁ and T₂ usually encountered in NMR and MRI measurements, the RF field B₁ may be on the order of ˜0.01 Gauss or less.

3-2. Magnetic Resonance Imaging (MRI)

The tasks of MRI applications are to obtain the spatial distributions, i.e., 1-D, 2-D or 3-D images of spin density ρ, spin-lattice relaxation time T₁, and spin-spin relaxation time T₂ of samples, such as tissues and human bodies, etc. The spin resonance frequency usually is a known parameter. To this end, a special apparatus or devices for spin spatial localization must be available prior to MRI measurements. This kind of apparatus may partially be adapted from the existing MRI system, or adapted from whatever means that can serve this spin localization purpose.

As conceptually illustrated in FIG. 5 a, this apparatus sorts out a thin rod-like slender volume 50 in a slice 52 of height z and thickness Δz. Along volume's longitudinal y dimension, a monotonic increasing (or decreasing), z-direction frequency-encoding magnetic field B_(e)(y) (54 in FIG. 5 b) is built up by the apparatus, so that each voxel with coordinate y in this slender volume is assigned a unique magnetic field B_(e)=B_(e)(y), and consequently a corresponding spin resonance frequency ν_(e)(y)=γ×[Bo+B_(e)(y)]/2π. In this way, each and every voxel in this volume can be localized by its unique spin emission frequency ν_(e)(y). Thus the 1-D resonance imaging can be realized. Sweeping this slender volume over the entire slice 52 generates a 2-D image; same sweeping fashion but for slices at various height z generates a 3-D image.

FIG. 6 shows the schematic of the MRI applications. Like the NMR applications in FIG. 4, block 60 is the MRI machine equipment including the two identical pairs of receiver (detection) coil sets surrounding the sample (FIG. 3) to induce two identical spin resonance emission noise signals V_(SRa)(t) and V_(SRb)(t) that, along with non-signal noise V_(n)(t) and B₁'s cross-coupling voltage U_(B1)(t), are fed to the electronics 62 and 64 (electronics 62 and 64 are identical). Note that although using the same symbols, the random noise voltage V_(na) and V_(nb) in the outputs of block 60 are less than the noise voltage V_(na) and V_(nb) in the output of electronic 62, and 64, since the latter contains the noises generated in the MRI machine block 60 plus the noises generated in the electronics blocks 62 and 64. The correlator 66 serves as auto-correlation for V_(SRa)(t)+U_(B1a) and V_(SRb)(t)+U_(B1b); but serves as cross-correlation for the random noises V_(na) and V_(nb). The correlation of V_(na) and V_(nb) equals zero due to their statistical independency. The auto-correlation function R′(t) from correlator 66 is the sum of auto-correlation R_(SR)(t) of V_(SR) and auto-correlation R_(B1)(t) of U_(B1). R_(B1)(t) is unwanted, and should be removed from R′(t). This is the task of the correction block 68. The output of correction block 66 is the auto-correlation function R(t) of the spin resonance emission noise signal V_(SR)(t), from which the MRI parameters can be derived as illustrated in FIG. 6. Because of the linearity of the Fourier transform and the statistical independency among all spin resonance emission noise signal V_(SRk)(t) of the k-th voxel, k=1, 2, . . . , N (N=total number of voxels in the volume 50 of FIG. 5), R(t) is the sum of all constituent auto-correction function R_(k)(t) of V_(SRk)(t). Each R_(k)(t) has a unique carrier frequency U_(k) depending on voxel's position y_(k) and B_(e)(y_(k)). This fact makes multichannel bandpass filtering 70 in FIG. 6 possible. The outputs of the filter 70 are separated R_(k)(t) for each k-th spin voxel, k=1, 2, . . . , N. T_(1k), T_(2k), S_(k)(ν), and ρ_(k) can then be derived from R_(k)(t), using the same procedures and equations as explained in the NMR section. T_(1k)=T₁(y_(k)), T_(2k)=T₂(y_(k)), and ρ_(k)=ρ(y_(k)), that is the 1-D imaging. The spatial resolution Δy in this 1-D image depends upon the gradient of field B_(e)(y) and the channel bandwidth Δν, Δy=2πΔν(dy/γdB_(e)).

As mentioned before, the obtained T₁, T₂, S(u), and p are their true values, not the “weighted” ones in the conventional pulsed NMR/MRI. Certainly, these true T₁, T₂, and p can be blended up using a pre-assigned mixing ratio to form any “weighted” imaging.

Both in FIG. 4 and FIG. 6, the electronics shown in the blocks 14, 16 and 62, 64 contains amplifiers, mixers, etc. A/D converters also can be included, or may be placed somewhere else.

4. Continuous Precision NMR/MRI Using One Single Receiver Coil

The foregoing descriptions are about using two identical receiver (detection) coil sets to generate two signals V_(a) and V_(b) that serve as two inputs to the auto-correlation. As a matter of fact, this continuous precision NMR/MRI technology can also be performed using one single receiver coil. In such cases, the receiver coils are the same as those employed in the conventional NMR/MRI machines.

FIGS. 7 a-7 c delineate three possible single-receiver-coil arrangements for the implementations of this continuous precision NMR/MRI method. The NMR/MRI signals come from the receiver coil 74, 76 or 78 of FIGS. 7 a-7 c. The other function blocks are the same as in FIG. 4 and FIG. 6. Those blocks that follow the blocks 82 are not shown in FIGS. 7 a-7 c.

The underlying principles of these three embodiments are the same with those utilizing twin identical receiver coils in FIGS. 4 and 6. The correction blocks 82 will be described in the next section.

The embodiment in FIG. 7 a is the simplest, yet its correlator 80 cannot eliminate any non-signal voltages generated in the coil itself and all electronics. Their effects will be removed in the correction block 82. The embodiment in FIG. 7 b cannot eliminate any non-spin signal noises from the coil itself and the pre-amplifier, but electronics noises generated in the block 94 can be eliminated in the correlator 86. The embodiment in FIG. 7 c cannot eliminate non-spin signal noises generated in the receiver coil itself, but all electronic noises from the electronics 88 and 90 are cancelled out in correlation 92. In FIG. 7 b, a path-length adjustment may be needed to compensate the path-length difference between the direct path and the path through the electronics 94. Without this compensation, the maximum R′(t) could appear a little bit away from t=0.

5. Correction of Correlation R′(t) for the Spin Resonance Emission Correlation R(t)

As shown in FIGS. 4, 6, and 7 a-7 c, the task for the correction block is to correct R′(t) to obtain R(t), i.e., to extract R(t) from R′(t). This may be stated in general as follows.

An auto-correlation function R′(t)=R(t)+R_(n)(t). R(t) and R_(n)(t) represent the auto-correlation functions of a random (or deterministic) signal V(t) and another random (or deterministic) signal V_(n)(t), respectively. V(t) must be statistically independent to V_(n)(t). Without losing generality, assume the power spectra of V(t) and V_(n)(t) are both of Lorentzian profiles (or other profiles), further assume the spectral bandwidth for V_(n)(t) is much wider, say ˜3 orders of magnitude wider, than the bandwidth for V(t). Thus, according to the reciprocity inequality for relaxation time and spectral bandwidth [13], the damping-off rate (or the relaxation time) of R_(n)(t) is much quicker, ˜3 orders of magnitude quicker (or shorter), than the damping-off rate (or the relaxation time) of R(t).

FIGS. 8 a-8 c shows these features. FIGS. 8 a and 8 b plot the R(t) curve of V(t) and the R_(n)(t) curve of V_(n)(t). Only the envelopes of their positive half are plotted for clarity. In the figures, relaxation time=0.1 sec for V(t) and relaxation time=0.0002 sec for V_(n)(t). Hence, the damping-off rate of R_(n)(t) is 500-fold faster than that of R(t). At t 0.0015 sec, R(t) virtually equals R(0), but R_(n)(t) already asymptotes to 0, although intentionally setting R_(n)(0)=100×R(0) (FIG. 8 c). In FIG. 8 c, curve #1 (a′-b′-c-d-e) is R(t)+R_(n)(t), derived from measurement data; curve #2 (a-b-c-d-e) is R(t)—the one ought to be extracted from curve #1. (Note the coordinate scales are very different in FIG. 8 a and FIG. 8 b.) Significant differences between curve #1 and #2 only occur in the immediate vicinity around t=0.

Therefore, a three-step correction procedure can be carried out as follows:

(1) Discard the segment of the correlation function R′(t) derived from the measurements from t=0 (point a) to t=t_(c) (point c). Having known the bandwidth of V_(n)(t), t_(c) can be well estimated. In FIG. 8 c, t_(c) may take around 0.002 sec.

(2) Find a curve equation numerically through curve-fitting based on the R′(t) data from point c to point e in FIG. 8 c.

(3) Extrapolate R′(t) numerically from point c to point a (t=0) using the curve equation obtained in step (2). Now this R′(t) is the corrected one, equal to R(t) at every time moment.

In the above description, V(t) represents the nuclear spin magnetic resonance emission signal V_(SR)(t), V_(n)(t) represents all non-spin signal noise V_(noise)(t) plus the B₁-related voltage U_(B1)(t). In NMR and MRI, the bandwidths of spin signal V_(SR)(t) are very narrow, generally from few tenth Hz to few tens Hz. The bandwidths of electronics noises V_(noise)(t) are easily a few orders of magnitude wider than the bandwidths of spin signal V_(SR)(t). In MRI, the bandwidth of the RF field B₁ has to cover the spin resonance frequencies of all voxels in volume 50 of FIG. 5, thus the bandwidth of V_(B1)(t) can also be a few orders wider than the bandwidths of spin signals V_(SR)(t). In NMR, the bandwidth of V_(B1)(t) can be purposely made a few orders wider than the bandwidths of spin signal V_(SR)(t). In each of the above cases, this correction scheme works with satisfaction.

6. Two Especial Features of the Continuous Precision NMR and MRI

One particularly advantageous feature of the present invention is seen in MRI applications. A RF field B₁ on the order of 0.01 Gauss means that the RF power deposited into a patient's body that is under MRI procedure only amounts to less than 10⁻⁸ of the RF power deposited into a patient's body in pulsed MRI. A RF power reduction factor of 10⁻⁸ is of vital significance in terms of patient safety issue.

Another advantageous feature is seen in NMR applications. Because this is a continuous operating method, the spin resonance emission signal can be measured as long as requested. According to the fast Fourier transform, the spectral resolution of a spectrum is inversely proportional to the available length of time of the measured signal. Hence, for example, a 100 or 1000 second-long signal may result in 0.01 or 0.001 Hz resolution, respectively. Such hyperfine resolutions have significant utility in NMR research.

7. The Continuous Precision ESR

Parallel to nuclear spin magnetic resonance, there is electron spin magnetic resonance (ESR). Similar to NMR, electron spin magnetic resonance is also a spectroscopic technique that detects species having unpaired electrons, but it is not as widely used as NMR. NMR and ESR share the same basic theories and technical concepts. One apparent difference of NMR and ESR is the resonance frequency: radio frequencies for NMR and microwave frequencies for ESR. Therefore, the method of the present invention also can be applied to electron spin magnetic resonance (ESR). In doing so, of course, the electronics will need to be modified to suit the microwave environment.

REFERENCES

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1. A method for NMR/MRI or ESR/MRI investigation of a target which comprises subjecting the target to MRI and ESR investigation or NMR and MRI investigation, mating spin resonance emission noise signals from said respective MRI and ESR or NMR and MRI investigations, and correlating the signals to eliminate noise and collecting signal data.
 2. The method of claim 1, wherein the MRI/ESR or NMR/MRI investigations are run continuously.
 3. The method of claim 1, including the step of filtering the signals to eliminate noise.
 4. The method of claim 3, wherein the signals are correlated to eliminate non-spin signal noise.
 5. The method of claim 1, including the step of applying a transverse RF magnetic field to stimulate extra spin resonance transition emission and to measure relaxation times T₁ and T₂.
 6. The method of claim 1, including the step of employing continuous stationary random noise as signals from nuclear spin magnetic resonance emissions of targets under investigation.
 7. The method of claim 1, including the step of detecting spin magnetic resonance emission noise with a single receiver coil set or two identical sets of receiver coils.
 8. The method of claim 1, which comprises using auto- and cross-correlation to enhance spin emission signal noise and eliminate other non-signal noise.
 9. The method of claim 1, further comprising purifying contaminated correlation function to obtain an auto-correlation function of spin magnetic resonance emissions.
 10. The method of claim 9, further comprising filtering the auto-correlation function to obtain constituent auto-correlation functions of each spin voxal in the target.
 11. The method of claim 9, further comprising precision data-processing the auto-correlation function of said spin resonance emissions to obtain true and accurate spin resonance power spectrum S(ν), spin density ρ and spin relaxation times T₁ and T₂ in said NMR application.
 12. The method of claim 9, further comprising precision data-processing and constituent auto-correlation functions of each voxel to obtain true and accurate 1-D, 2-D and 3-D imaging of spin density ρ and spin relaxation dines T₁ and T₂ in said MRI application.
 13. An MRI/ESR or NMR/MRI system for investigation of a target comprising in combination twin pairs of coils for generating twin spin resonance emission signals, and filters and correlators for correlating signals from said coils.
 14. The system of claim 13, wherein said system runs continuously during said investigation.
 15. The system of claim 14, further including a filter for filtering and correlating signals are filtered and correlated to eliminate non-spin signals.
 16. The system of claim 13, wherein said filter comprises a multi-channel bandpass filter.
 17. The system of claim 13, comprising two identical pairs of receiver coil sets placed on two sides surrounding the target.
 18. The system of claim 13, wherein the coils comprise a pair of coils wound together around the target.
 19. The system of claim 13, further comprising computer readable computer code for correcting signals as part of said correlation.
 20. A method of continuously performing nuclear spin magnetic resonance of a target, comprising: generating continuous spin magnetic resonance random emission noise signals; intercepting and receiving the spin resonance emission noise signals; conditioning and AD (analog-to-digital) converting the spin resonance noise signals; correlating and spectral analyzing the spin resonance noise signals for obtaining a correlation function and power spectrum; correcting the acquired correlation function to eliminate effects of non-spin signals and to extract the correlation function of the spin resonance noise signal; and retrieving spin magnetic resonance parameters and their 1-D, 2-D, and 3-D images from the acquired correlation function or power spectrum.
 21. A method of continuously performing nuclear spin magnetic resonance of a target, comprising: applying a steady continuous radio-frequency (RF) magnetic field B₁, transverse to a field B₀ direction wherein the strength of the RF is much weaker than the strength of the field B₀.
 22. A method of performing Magnetic Resonance Imaging of a target, comprising: applying a frequency-encoding magnetic gradient field B_(c) that holds unchanged with time during a measurement, the direction of the field B_(e) being the same as the direction of a static field B_(o).
 23. A nuclear spin magnetic resonance system, comprising a detection device, wherein the detection device comprises identical dual sets of receiver coils for inducing two identical spin resonance emission noise signals at their two pairs of coil terminals.
 24. A nuclear spin magnetic resonance system comprising a detection device, wherein the detection device comprises a single set of receiver coils for inducing a spin resonance emission noise signal at the coil terminals.
 25. The method of claim 20, further comprising continuous and direct utilization of the target's spin magnetic resonance emission noises from the detection device as time domain NMR or MRI signals.
 26. The method of claim 20, further comprising: generating dual sets of NMR signals by placing the target in a static field B₀ and applying a transverse RF field B₁; receiving two sets of spin resonance random emission signals and non-spin signals using identical dual sets of receiver coils, wherein the two sets of spin resonance emission signals are identical.
 27. The method of claim 20, further comprising: generating a single set of NMR signals by placing the target in a static field B₀, applying a transverse RF field B₁, and receiving spin resonance random emission signal and non-spin signals using a single set of receiver coils.
 28. The method of claim 20, further comprising: generating dual sets of MRI signals by placing the target in a static field B_(o); applying a transverse RF field B₁ and a frequency-encoding field B_(e); and receiving two identical sets of spin resonance random emission signals and non-spin signals using identical dual sets of receiver coils.
 29. The method of claim 20, further comprising: generating a single set of MRI signals by placing the target in a static field B_(o), and applying a transverse RF field B₁ and a frequency-encoding field B_(e); and receiving spin resonance emission signal and non-spin signals using a single set of receiver coils.
 30. The method of claim 20, further comprising: using dual sets of receiver coils; conditioning dual sets of signals using two sets of same electronics, one set of electronics for one set of signals wherein the two sets of electronics output two sets of conditioned spin resonance signals along with two sets of non-spin signals; and AD (analog-to-digital) converting, using two ADC (analog-to-digital converters), one ADC for one set of signals.
 31. The method of claim 20, further comprising using a single set of receiver coils; conditioning the single set of signals using two sets of same electronics; and AD (analog-to-digital) converting, using two ADCs.
 32. The method of claim 20, wherein acquiring the correlation function and the power spectrum comprises: acquiring the correlation function first and the power spectrum second; correlating the conditioned signals, which contain both spin resonance emission signals and all non-spin signals, to obtain correlation function R′(t); correcting the contaminated correlation function R′(t) to extract the desired correlation function R(t) of spin resonance random emission signal; and acquiring the spin resonance power spectrum S(ν) from the spin resonance correlation function R(t) by applying the Fourier transform.
 33. The method of claim 20, wherein acquiring the correlation function and the power spectrum comprises: acquiring the power spectrum first, and the correlation function second; acquiring power spectrum S′(ν) based on the conditioned signals, obtaining a contaminated correlation function R′(t) from a contaminated power spectrum S′(ν) by applying the Fourier transform; correcting the contaminated correlation function R′(t) to extract a desired correlation function R(t) of spin resonance random emission signals; and obtaining a desired power spectrum S(ν) of spin resonance emission noise signal from the correlation function R(t) by applying the Fourier transform.
 34. The method of claim 33, wherein retrieving the NMR parameters comprises: acquiring (relative) spin number density ρ, spin resonance frequency ν_(o), spin-lattice relaxation time T₁ and spin-spin relaxation time T₂ by solving related equations and expressions based on the obtained correlation function R(t) or power spectrum S(ν).
 35. The method of claim 33, wherein retrieving MRI parameters comprises: decomposing the acquired correlation function R(t) or power spectrum S(ν) into their components through multichannel bandpass filtering, each component R(t) or S(ν) belonging to a corresponding voxel in the sample; and acquiring 1-D, 2-D, or 3-D images of MRI parameters by repeatedly solving related equations and expressions for each voxel in the sample based on the obtained component correlation functions or power spectra. 